SEVERAL recent papers1-3 have refocused attention on the question of the degree of dust obscuration (or optical depth) of the disks of spiral galaxies. The traditional view, based on the early statistical studies of Holmberg4 and de Vaucouleurs5, is that the disks are largely transparent, whereas Disney et al.1 and Valentijn2 have recently argued in favour of substantial optical depths. In an attempt to resolve this issue, White and Keel3 measured the broad-band colours of an overlapping galaxy pair, to determine directly the optical depth of the foreground galaxy; however, using this method it was not possible to separate unambiguously the contributions from the two galaxies. Individual emission lines, on the other hand, are completely separated if the redshift difference between the two galaxies is large enough, as in the pair studied here, offering a means of removing the source ambiguity. By comparing the Halpha/Hbeta ratios for the H II regions in the background galaxy with those in isolated spiral galaxies, and exploiting the wavelength dependence of extinction by dust, we find significant optical depths along three lines of sight through the foreground galaxy.